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Display information for equation id:math.2092.5 on revision:2092

* Page found: Magnetostatische Feldgleichungen (eq math.2092.5)

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Magnetostatische Feldgleichungen Eq: math.2095.5

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\begin{align}
& rot\bar{A}(\bar{r})=\nabla \times \frac{{{\mu }_{0}}}{4\pi }\int_{{{R}^{3}}}^{{}}{{}}{{d}^{3}}r\acute{\ }\frac{\bar{j}(\bar{r}\acute{\ })}{\left| \bar{r}-\bar{r}\acute{\ } \right|}=\frac{{{\mu }_{0}}}{4\pi }\int_{{{R}^{3}}}^{{}}{{}}{{d}^{3}}r\acute{\ }{{\nabla }_{r}}\frac{1}{\left| \bar{r}-\bar{r}\acute{\ } \right|}\times \bar{j}(\bar{r}\acute{\ }) \\
& {{\nabla }_{r}}\frac{1}{\left| \bar{r}-\bar{r}\acute{\ } \right|}=-\frac{\bar{r}-\bar{r}\acute{\ }}{{{\left| \bar{r}-\bar{r}\acute{\ } \right|}^{3}}} \\
& \Rightarrow rot\bar{A}(\bar{r})=\frac{{{\mu }_{0}}}{4\pi }\int_{{{R}^{3}}}^{{}}{{}}{{d}^{3}}r\acute{\ }\bar{j}(\bar{r}\acute{\ })\times \frac{\bar{r}-\bar{r}\acute{\ }}{{{\left| \bar{r}-\bar{r}\acute{\ } \right|}^{3}}}=\bar{B}(\bar{r}) \\
\end{align}

TeX (checked):

{\begin{aligned}&rot{\bar {A}}({\bar {r}})=\nabla \times {\frac {{\mu }_{0}}{4\pi }}\int _{{R}^{3}}^{}{}{{d}^{3}}r{\acute {\ }}{\frac {{\bar {j}}({\bar {r}}{\acute {\ }})}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}={\frac {{\mu }_{0}}{4\pi }}\int _{{R}^{3}}^{}{}{{d}^{3}}r{\acute {\ }}{{\nabla }_{r}}{\frac {1}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}\times {\bar {j}}({\bar {r}}{\acute {\ }})\\&{{\nabla }_{r}}{\frac {1}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}=-{\frac {{\bar {r}}-{\bar {r}}{\acute {\ }}}{{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}^{3}}}\\&\Rightarrow rot{\bar {A}}({\bar {r}})={\frac {{\mu }_{0}}{4\pi }}\int _{{R}^{3}}^{}{}{{d}^{3}}r{\acute {\ }}{\bar {j}}({\bar {r}}{\acute {\ }})\times {\frac {{\bar {r}}-{\bar {r}}{\acute {\ }}}{{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}^{3}}}={\bar {B}}({\bar {r}})\\\end{aligned}}

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\begin{matrix} r o t \bar{A} (\bar{r}) = \nabla \times \frac{μ_{0}}{4 π} \int_{R^{3}}^{} d^{3} r \overset{´}{} \frac{\bar{j} (\bar{r} \overset{´}{})}{| \bar{r} - \bar{r} \overset{´}{} |} = \frac{μ_{0}}{4 π} \int_{R^{3}}^{} d^{3} r \overset{´}{} \nabla_{r} \frac{1}{| \bar{r} - \bar{r} \overset{´}{} |} \times \bar{j} (\bar{r} \overset{´}{}) \\ \nabla_{r} \frac{1}{| \bar{r} - \bar{r} \overset{´}{} |} = - \frac{\bar{r} - \bar{r} \overset{´}{}}{{| \bar{r} - \bar{r} \overset{´}{} |}^{3}} \\ \Rightarrow r o t \bar{A} (\bar{r}) = \frac{μ_{0}}{4 π} \int_{R^{3}}^{} d^{3} r \overset{´}{} \bar{j} (\bar{r} \overset{´}{}) \times \frac{\bar{r} - \bar{r} \overset{´}{}}{{| \bar{r} - \bar{r} \overset{´}{} |}^{3}} = \bar{B} (\bar{r}) \end{matrix}

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Identifiers

$r$

$o$

$t$

$\bar{A}$

$\bar{r}$

$μ_{0}$

$π$

$R$

$r$

$\overset{´}{}$

$\bar{j}$

$\bar{r}$

$\overset{´}{}$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$μ_{0}$

$π$

$R$

$r$

$\overset{´}{}$

$r$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$\bar{j}$

$\bar{r}$

$\overset{´}{}$

$r$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$r$

$o$

$t$

$\bar{A}$

$\bar{r}$

$μ_{0}$

$π$

$R$

$r$

$\overset{´}{}$

$\bar{j}$

$\bar{r}$

$\overset{´}{}$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$\bar{B}$

$\bar{r}$

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